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Understanding
9/11A Concise Introduction To Mathematical Logic 3rd Ed Wolfgang Rautenberg 2009
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A Concise Introduction To Mathematical Logic 3rd Ed Wolfgang Rautenberg 2009
- Publication date
- 2009
- Topics
- Logic, Mathematics, Lógica, Matemática
- Collection
- opensource
- Language
- English
- Item Size
- 143.0M
Traditional logic as a part of philosophy is one of the oldest scientific
disciplines. It can be traced back to the Stoics and to Aristotle2 and
is the root of what is nowadays called philosophical logic. Mathematical
logic, however, is a relatively young discipline, having arisen from the endeavors
of Peano, Frege, and Russell to reduce mathematics entirely to
logic. It steadily developed during the twentieth century into a broad discipline
with several subareas and numerous applications in mathematics,
computer science, linguistics, and philosophy.
One feature of modern logic is a clear distinction between object language
and metalanguage. The first is formalized or at least formalizable.
The latter is, like the language of this book, a kind of a colloquial language
that differs from author to author and depends also on the audience the
author has in mind. It is mixed up with semiformal elements, most of
which have their origin in set theory. The amount of set theory involved
depends on one’s objectives. Traditional semantics and model theory
as essential parts of mathematical logic use stronger set-theoretic tools
than does proof theory. In some model-theoretic investigations these are
often the strongest possible ones. But on average, little more is assumed
than knowledge of the most common set-theoretic terminology, presented
in almost every mathematical course or textbook for beginners. Much of
it is used only as a façon de parler.
...
- Addeddate
- 2020-08-01 14:30:43
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